CN111931293B - Method for calculating relative aging rate of lightweight vehicle-mounted traction transformer - Google Patents
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Abstract
The invention discloses a method for calculating the relative aging rate of a lightweight vehicle-mounted traction transformer, which comprises the following steps: the method comprises the steps of establishing a lightweight vehicle-mounted traction transformer axisymmetric two-dimensional model, arranging temperature monitoring nodes, calculating thermal resistances of all parts, distributing heating power for winding temperature nodes, solving winding temperature node temperature values, obtaining hot point temperatures and calculating relative aging rates. The invention has the beneficial effects that: compared with a computational fluid dynamics method which is complicated in modeling and consumes a large amount of computational resources and time, the method can realize efficient and rapid calculation of the relative aging rate of the lightweight vehicle-mounted traction transformer, provides a new means for optimizing the overall structure, improving the thermal characteristics and utilizing and regulating the load of the lightweight vehicle-mounted traction transformer, and reduces the consumption of manpower and material resources in the design and operation and maintenance processes.
Description
Technical Field
The invention relates to the field of electric insulation online detection and fault diagnosis, in particular to a method for calculating the relative aging rate of a light-weight vehicle-mounted traction transformer.
Background
The vehicle-mounted traction transformer is used as a core device of a traction system of the motor train unit, is responsible for the supply task of all electric energy of the motor train unit train, and has the performance which greatly influences the reliability and safety of the running of the whole motor train unit. A great part of faults of the transformer are caused by insulation failure, so that the relative aging rate of the transformer is efficiently acquired in the design stage, and the significance of accurately calculating the service life loss of the transformer under different design parameters, loads and special overload conditions is great.
The hot spot temperature is an important influence factor of the relative aging rate of the transformer, so the hot spot temperature of the transformer must be accurately known. The light-weight vehicle-mounted traction transformer cancels components such as an oil tank and insulating oil, the weight is far lower than that of an oil-immersed vehicle-mounted traction transformer, but the heat dissipation condition is more severe and the load loss is far higher than that of a ground transformer with the same capacity, so that the relative aging rate of the light-weight vehicle-mounted traction transformer needs to be accurately calculated. Computational fluid dynamics is a common means for calculating the hot spot temperature of a transformer, has high calculation accuracy, can provide abundant flow and heat transfer detail data, has huge consumption on time and computer resources, and has certain limitation on occasions requiring a large amount of tentative calculation, such as transformer design and the like. Therefore, a rapid and batch calculation method for the hotspot temperature of the lightweight vehicle-mounted traction transformer is urgently needed, so that the relative aging rate of the transformer can be efficiently obtained, technical means support is provided for the optimized design of the overall structure, the improvement of the thermal characteristic and the reasonable arrangement of the operation and the running of the train after the operation, and the aims of ensuring the running safety of the high-speed motor train unit, prolonging the service life of the vehicle-mounted traction transformer and improving the production economy of a manufacturer are fulfilled.
Disclosure of Invention
In view of the above technical problems, the present invention aims to provide a method for calculating the relative aging rate of a light-weight vehicle-mounted traction transformer, which can realize the rapid calculation of the relative aging rate of the light-weight vehicle-mounted traction transformer.
The technical scheme for realizing the purpose of the invention is as follows:
a method for calculating the relative aging rate of a lightweight vehicle-mounted traction transformer is characterized by comprising the following steps:
firstly, establishing an axisymmetric two-dimensional model of a lightweight vehicle-mounted traction transformer
Carrying out primary treatment according to the structural characteristics of the lightweight vehicle-mounted traction transformer: structures with small influence on temperature distribution, such as winding outlet terminals, clamps, stays and the like, are deleted, and a cooling air duct is simplified into an annular pipeline with constant heat flow on the inner wall surface and the outer wall surface simultaneously or independently;
secondly, arrange the temperature monitoring node, the temperature monitoring node includes: the winding temperature nodes, the insulating paper boundary nodes, the epoxy resin boundary nodes and the air temperature nodes are connected through thermal resistance to form a lightweight vehicle-mounted traction transformer thermal network model; the node arrangement method specifically comprises the following steps:
1) 1 winding temperature node is arranged at the center of each turn of the winding conductor, and the winding temperature nodes are aligned in the axial direction and the radial direction according to the winding structure;
2) 4 insulation paper boundary nodes are respectively arranged in the upper, lower, left and right 4 directions of the winding temperature node;
3) 2 epoxy resin boundary nodes are respectively arranged on the upper side and the lower side of the upper insulating paper boundary node and the lower insulating paper boundary node;
4) 1 air temperature node is arranged between 2 epoxy resin boundary nodes on two sides of the cooling air channel;
5) the winding temperature nodes are connected with the insulating paper boundary nodes through insulating paper thermal resistances, the insulating paper boundary nodes are connected with the epoxy resin boundary nodes through epoxy resin thermal resistances, the epoxy resin boundary nodes are connected with the air temperature nodes through convective thermal resistances, and the air temperature nodes are connected through air thermal resistances;
thirdly, calculating the thermal resistance of each part
1) Thermal resistance R of insulating paperpCalculated using the following formula:
in the formula, kpIs the thermal conductivity (W.m) of the insulating paper-1·k-1)，lpIs the thickness (m) of the insulating paper in the direction of heat flow of the thermal resistance of the insulating paper, SpThe contact area (m) of the insulating paper and the copper conductor in the heat flow direction of the thermal resistance of the insulating paper2)；
2) Thermal resistance R of epoxy resineCalculated using the following formula:
in the formula, keIs the thermal conductivity (W.m) of the epoxy resin-1·k-1)，leIs the thickness (m), S, of the epoxy resin in the heat flow direction of the epoxy resin heat resistanceeThe contact area (m) of the epoxy resin and the insulating paper in the heat flow direction of the epoxy resin heat resistance2)；
3) Air thermal resistance RairUse ofCalculated by the following formula:
in the formula, mairMass flow (kg.s) of air in cooling duct-1)，Cp_airThe specific heat capacity (J.kg) of air-1·K-1)，LductIs the total length (m) of the cooling air duct, and l is the axial width (m) of the conductor;
4) convective heat resistance RconvCalculated using the following formula:
in the formula, DoIs the outer diameter (m), D of the cooling air ductiIs the inner diameter (m) of the cooling air duct, NuxIs a local Nussel number, kairIs the thermal conductivity (W.m) of air-1·k-1)，SductThe contact area (m) of the epoxy resin outside the temperature node of a single winding and the cooling air duct2)；
The convective thermal resistance RconvIn the formula (2), NuxThe calculation formula of (a) is as follows:
in the formula, n is the number of the winding temperature node, and the rule is as follows: the winding temperature node at the inlet of the innermost cooling air duct is numbered as No. 1, and the winding temperature nodes from the inlet of the innermost cooling air duct to the outlet of the outermost cooling air duct are numbered as 2, 3 and 4 … in sequence; x is the distance (m) from the air duct inlet, R is the central line radius (m) of the cooling air duct, Re is the Reynolds number of the cooling air duct, and the Reynolds number is calculated by using the following formula:
in the formula (I), the compound is shown in the specification,ρ is the air density (kg. m)-3) V is the air flow velocity (m · s)-1) μ is aerodynamic viscosity (kg · m)-1·s-1)；
Fourthly, distributing heating power for winding temperature nodes
The heating power distributed to the winding temperature node with the number n is calculated according to the following formula:
in the formula, VnConductor volume (m) corresponding to winding temperature node numbered n3)，VGeneral assemblyIs the total volume (m) of the winding3) Q is a loss value (W) under the relative aging rate to be solved;
fifthly, solving the temperature of the winding temperature nodes according to the lightweight vehicle-mounted traction transformer thermal network model structure from the first step to the fourth step and a kirchhoff law sequence writing node voltage equation to obtain temperature values of all the winding temperature nodes;
sixthly, obtaining a winding temperature node with the highest temperature according to the temperature calculation result of the winding temperature node obtained in the fifth step, wherein the temperature of the node is the hot spot temperature and is recorded as Ths；
And seventhly, calculating the relative aging rate of the lightweight vehicle-mounted traction transformer, wherein the formula is as follows:
wherein V is a relative aging rate.
The method for calculating the relative aging rate of the light-weight vehicle-mounted traction transformer has the following advantages:
1) the relative aging rate of the light-weight vehicle-mounted traction transformer can be accurately calculated, a new means is provided for the design of the light-weight vehicle-mounted traction transformer, and the optimization design of the whole structure, the improvement of the thermal characteristics and the regulation and control of load utilization are facilitated;
2) compared with a computational fluid dynamics method, the computational method of the relative aging rate is simpler and faster in modeling, the time consumed by computation and computer resources are greatly reduced, the working efficiency of the computation of the relative aging rate can be effectively improved, and the consumption of manpower and material resources is reduced.
Drawings
FIG. 1 is a flow chart of a method for calculating the relative aging rate of a lightweight vehicle-mounted traction transformer according to the present invention;
FIG. 2 is a schematic diagram of structural parameters of a lightweight vehicle-mounted traction transformer to be analyzed;
FIG. 3 is an axisymmetric two-dimensional model of a lightweight on-board traction transformer to be analyzed;
FIG. 4 is a schematic view of a temperature monitoring node arrangement local to a lightweight on-board traction transformer;
FIG. 5 is a graph of temperature values and hot spot temperatures versus position for all winding temperature nodes.
Detailed Description
The invention is further described with reference to the accompanying drawings and the specific implementation procedures. It should be emphasized that the embodiments described herein are merely illustrative of the invention and do not limit the scope of the inventive concept and its claims.
Firstly, establishing an axisymmetric two-dimensional model of a lightweight vehicle-mounted traction transformer
The method comprises the following steps of obtaining structural parameters (see figure 2) of a certain lightweight vehicle-mounted traction transformer to be analyzed, carrying out two-layer winding and 168 turns of conductor, and carrying out primary treatment according to the characteristics: deleting structures with small influence on temperature distribution, such as winding outlet terminals, clamps, stays and the like, simplifying a cooling air duct into an annular pipeline with inner and outer wall surfaces having constant heat flow simultaneously or independently, and finally establishing a corresponding axisymmetric two-dimensional model (see fig. 3);
secondly, arrange the temperature monitoring node, the temperature monitoring node includes: the winding temperature nodes, the insulating paper boundary nodes, the epoxy resin boundary nodes and the air temperature nodes are connected through thermal resistance to form a lightweight vehicle-mounted traction transformer thermal network model; the node arrangement method is specifically as follows (see fig. 4):
1) 1 winding temperature node is arranged at the center of each turn of the winding conductor, and the winding temperature nodes are aligned in the axial direction and the radial direction according to the winding structure;
2) 4 insulation paper boundary nodes are respectively arranged in the upper, lower, left and right 4 directions of the winding temperature node;
3) 2 epoxy resin boundary nodes are respectively arranged on the upper side and the lower side of the upper insulating paper boundary node and the lower insulating paper boundary node;
4) 1 air temperature node is arranged between 2 epoxy resin boundary nodes on two sides of the cooling air channel;
5) the winding temperature nodes are connected with the insulating paper boundary nodes through insulating paper thermal resistances, the insulating paper boundary nodes are connected with the epoxy resin boundary nodes through epoxy resin thermal resistances, the epoxy resin boundary nodes are connected with the air temperature nodes through convective thermal resistances, and the air temperature nodes are connected through air thermal resistances;
thirdly, calculating the thermal resistance of each part
1) Thermal resistance R of insulating paperpCalculated using the following formula:
in the formula, kpIs the thermal conductivity (W.m) of the insulating paper-1·k-1)，lpIs the thickness (m) of the insulating paper in the direction of heat flow of the thermal resistance of the insulating paper, SpThe contact area (m) of the insulating paper and the copper conductor in the heat flow direction of the thermal resistance of the insulating paper2)；
2) Thermal resistance R of epoxy resineCalculated using the following formula:
in the formula, keIs the thermal conductivity (W.m) of the epoxy resin-1·k-1)，leIs the thickness (m) of the epoxy resin in the heat flow direction of the epoxy resin heat resistance)，SeThe contact area (m) of the epoxy resin and the insulating paper in the heat flow direction of the epoxy resin heat resistance2)；
3) Air thermal resistance RairCalculated using the following formula:
in the formula, mairMass flow (kg.s) of air in cooling duct-1)，Cp_airThe specific heat capacity (J.kg) of air-1·K-1)，LductIs the total length (m) of the cooling air duct, and l is the axial width (m) of the conductor;
4) convective heat resistance RconvCalculated using the following formula:
in the formula, DoIs the outer diameter (m), D of the cooling air ductiIs the inner diameter (m) of the cooling air duct, NuxIs a local Nussel number, kairIs the thermal conductivity (W.m) of air-1·k-1)，SductThe contact area (m) of the epoxy resin outside the temperature node of a single winding and the cooling air duct2)；
The convective thermal resistance RconvIn the formula (2), NuxThe calculation formula of (a) is as follows:
in the formula, n is the number of the winding temperature node, and the rule is as follows: the winding temperature node at the inlet of the innermost cooling air duct is numbered as No. 1, and the winding temperature nodes from the inlet of the innermost cooling air duct to the outlet of the outermost cooling air duct are numbered as 2, 3 and 4 … in sequence; x is the distance (m) of air leaving the inlet of the cooling air duct, R is the radius (m) of the central line of the cooling air duct, Re is the Reynolds number of the cooling air duct, and the Reynolds number is calculated by using the following formula:
wherein ρ is an air density (kg · m)-3) V is the air flow velocity (m · s)-1) μ is aerodynamic viscosity (kg · m)-1·s-1)；
Fourthly, distributing heating power for winding temperature nodes
The heating power distributed to the winding temperature node with the number n is calculated according to the following formula:
in the formula, VnConductor volume (m) corresponding to winding temperature node numbered n3)，VGeneral assemblyIs the total volume (m) of the winding3) Q is a loss value (W) under the relative aging rate to be solved;
fifthly, according to the heat network model structure of the light-weight vehicle-mounted traction transformer from the first step to the fourth step, writing a node voltage equation according to kirchhoff's law, solving the temperature of the winding temperature nodes by using MATLAB programming, and obtaining the temperature values of all the winding temperature nodes (see figure 5);
sixthly, acquiring a winding temperature node with the highest temperature, namely the number 161, according to the temperature calculation result of the winding temperature node in the fifth step, wherein the hot spot temperature is 169.488 ℃;
and seventhly, calculating the relative aging rate of the lightweight vehicle-mounted traction transformer, wherein the formula is as follows:
the relative aging rate of the lightweight vehicle-mounted traction transformer is 3.74 e-22.
Claims (1)
1. A method for calculating the relative aging rate of a lightweight vehicle-mounted traction transformer is characterized by comprising the following steps:
firstly, establishing an axisymmetric two-dimensional model of a lightweight vehicle-mounted traction transformer
Carrying out primary treatment according to the structural characteristics of the lightweight vehicle-mounted traction transformer: deleting winding outlet terminals, clamping pieces and supporting strip structures, and simplifying a cooling air duct into an annular pipeline with constant heat flow on the inner wall surface and the outer wall surface;
secondly, arrange the temperature monitoring node, the temperature monitoring node includes: the winding temperature nodes, the insulating paper boundary nodes, the epoxy resin boundary nodes and the air temperature nodes are connected through thermal resistance to form a lightweight vehicle-mounted traction transformer thermal network model; the node arrangement method specifically comprises the following steps:
1) 1 winding temperature node is arranged at the center of each turn of the winding conductor, and the winding temperature nodes are aligned in the axial direction and the radial direction according to the winding structure;
2) 4 insulation paper boundary nodes are respectively arranged in the upper, lower, left and right 4 directions of the winding temperature node;
3) 2 epoxy resin boundary nodes are respectively arranged on the upper side and the lower side of the upper insulating paper boundary node and the lower insulating paper boundary node;
4) 1 air temperature node is arranged between 2 epoxy resin boundary nodes on two sides of the cooling air channel;
5) the winding temperature nodes are connected with the insulating paper boundary nodes through insulating paper thermal resistances, the insulating paper boundary nodes are connected with the epoxy resin boundary nodes through epoxy resin thermal resistances, the epoxy resin boundary nodes are connected with the air temperature nodes through convective thermal resistances, and the air temperature nodes are connected through air thermal resistances;
thirdly, calculating the thermal resistance of each part
1) Thermal resistance R of insulating paperpCalculated using the following formula:
in the formula, kpIs the thermal conductivity of the insulating paper, in W·m-1·K-1，lpThe thickness of the insulating paper in the direction of heat flow of the thermal resistance of the insulating paper is given in m, SpThe contact area of the insulating paper and the copper conductor in the heat flow direction of the thermal resistance of the insulating paper is m2；
2) Thermal resistance R of epoxy resineCalculated using the following formula:
in the formula, keIs the thermal conductivity of the epoxy resin and has the unit of W.m-1·K-1，leIs the thickness of the epoxy resin in the heat flow direction of the epoxy resin thermal resistance and has a unit of m, SeThe contact area of the epoxy resin and the insulating paper in the heat flow direction of the epoxy resin heat resistance is m2；
3) Air thermal resistance RairCalculated using the following formula:
in the formula, mairIs the mass flow of air in the cooling air duct, and has the unit of kg.s-1，Cp_airIs the specific heat capacity of air, and has a unit of J.kg-1·K-1，LductThe unit is m for the total length of the cooling air duct, and l is the axial width of the conductor and the unit is m;
4) convective heat resistance RconvCalculated using the following formula:
in the formula, DoIs the outer diameter of the cooling air duct, and has the unit of m and DiIs the inner diameter of the cooling air duct, and the unit is m, NuxIs a local Nussel number, kairIs the thermal conductivity of air, and has the unit of W.m-1·K-1，SductThe contact area of the epoxy resin outside the temperature node of a single winding and the cooling air duct is m2；
The convective thermal resistance RconvIn the formula (2), NuxThe calculation formula of (a) is as follows:
in the formula, n is the number of the winding temperature node, and the rule is as follows: the winding temperature node at the inlet of the innermost cooling air duct is numbered as No. 1, and the winding temperature nodes from the inlet of the innermost cooling air duct to the outlet of the outermost cooling air duct are numbered as 2, 3 and 4 … in sequence; x is the distance from the air duct inlet, and the unit is m, R is the center line radius of the cooling air duct, the unit is m, and Re is the Reynolds number of the cooling air duct, and the following formula is used for calculating:
where ρ is the air density in kg · m-3V is the air flow rate in m.s-1Mu is aerodynamic viscosity in kg.m-1·s-1；
Fourthly, distributing heating power for winding temperature nodes
The heating power distributed to the winding temperature node with the number n is calculated according to the following formula:
in the formula, VnConductor volume corresponding to winding temperature node numbered n in m3，VGeneral assemblyIs the total volume of the winding, in m3Q is a loss value under the relative aging rate to be solved, and the unit is W;
fifthly, solving the temperature of the winding temperature nodes according to the lightweight vehicle-mounted traction transformer thermal network model structure from the first step to the fourth step and a kirchhoff law sequence writing node voltage equation to obtain temperature values of all the winding temperature nodes;
sixthly, obtaining a winding temperature node with the highest temperature according to the temperature calculation result of the winding temperature node obtained in the fifth step, wherein the temperature of the node is the hot spot temperature and is recorded as Ths；
And seventhly, calculating the relative aging rate of the lightweight vehicle-mounted traction transformer, wherein the formula is as follows:
wherein V is a relative aging rate.
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